{
  "id": "2101.04946",
  "version": "v1",
  "published": "2021-01-13T09:17:46.000Z",
  "updated": "2021-01-13T09:17:46.000Z",
  "title": "An arbitrary-order discrete de Rham complex on polyhedral meshes. Part II: Consistency",
  "authors": [
    "Daniele Antonio Di Pietro",
    "Jérôme Droniou"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper we prove a complete panel of consistency results for the discrete de Rham (DDR) complex introduced in the companion paper [D. A. Di Pietro and J. Droniou, An arbitrary-order discrete de Rham complex on polyhedral meshes. Part I: Exactness and Poincar\\'e inequalities, 2021, submitted], including primal and adjoint consistency for the discrete vector calculus operators, and consistency of the corresponding potentials. The theoretical results are showcased by performing a full convergence analysis for a DDR approximation of a magnetostatics model. Numerical results on three-dimensional polyhedral meshes complete the exposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-13T09:17:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N99",
      "78A30"
    ],
    "keywords": [
      "rham complex",
      "arbitrary-order discrete",
      "consistency",
      "three-dimensional polyhedral meshes complete",
      "discrete vector calculus operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}